Selection for Multivariate Copula Based on Conditional Probability Integral Transformation
Notice bibliographique
Résumé
The dependence structure among multivariate financial assets is a critical factor for achieving accuracy in the integrated risk measurement.Copula function is a very useful tool to describe the dependence structure between risk factors and plays an important role in the field of financial risk management.When using the Copula model,the most important thing is to judge which Copula is more suitable to describe the data dependence structure.Therefore,it is very important to do research on the selection criteria of multivariate Copula models and the goodness-of-fit test methods.However,in the field of financial risk management,most of the research has focused on bivariate cases.There is very little research on the goodness-of-fit and empirical analysis on the multivariate cases.There is still no effective solutions for the selection and goodness-of-fit test of multivariate Copula functions. Therefore,this paper proposes a selection criterion for Copula's goodness-of-fit based on the method of conditional probability integral transformation.We analyze and compare the Anderson-Darling(AD),Kolmogorov-Smirnov(KS) and Cramer-von Mises(CM) test statistics under the CPIT method with various sample sizes and different variable dimensions.In addition,we use daily data of three stock indices: SP/TSX Composite index(GSPTSE) in Canada's stock market,INMEX.MX in Mexico's stock market and NASDAQ-100(NDX) in America's stock market.Our samples consist of 1606 adjusted-closing price in each of the three indices.We compare the CPIT test statistics with two other methods based on kernel the density estimate and the maximum likelihood estimate. The empirical studies results show that in terms of the power of goodness-of-fit test,the approach we proposed has a better performance.This method is able to solve the puzzle in selecting multivariate Copula models and its goodness-of-fit test is accurate and stable.Specifically,CM test statistic is more powerful in small samples;however in large samples the test is weaker than AD and KS tests.We also show that the AD test has a strong testing ability in large samples.On the other hand,the statistics based on the kernel density estimate method is more appropriate for selecting the best Copula functions under a large sample.The reason is that in a large sample,the kernel function selection has little effect on the estimated distribution.However,in a small sample,the choice of bandwidth in kernel estimation has a big effect on the estimation of marginal distribution,which may result in an unstable result.Although the test based on maximum likelihood estimate is able to choose Gauss Copula function as the best Copula to describe the correlation pattern between datasets,the method is quite unstable.As a result,its capacity of choosing the optimal Copula function is relatively weak.
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule tête enseignante, pas un consensus.
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